FRACTAL DIMENSION OF SPIN-GLASSES INTERFACES IN DIMENSION d = 2 AND d = 3 VIA STRONG DISORDER RENORMALIZATION AT ZERO TEMPERATURE

Erratum: Dilute spin glass at zero temperature in general dimension

We study the zero-temperature critical behavior of the dilute Ising spin glass. In our model nearest-neighbor exchange interactions randomly assume the values +J, 0, -J with probabilities p/2, 1-p, and p/2, respectively. We have generated 15th-order series for the Edwards-Anderson spin-glass susceptibility as a function of concentration p on hypercubic lattices in general dimension. Their analy...

Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Spin stiffness and lower critical dimension of vector spin glasses

Considerable advances have been made in recent years in the understanding of Ising spin glass models in two and three dimensions. Models with continuous degrees-of-freedom, which are often more realistic in describing physical systems, have received much less attention. We study properties of domain-wall excitations in continuous-spin glass systems by means of extensive numerical ground-state c...

Fractal Intersections and Products via Algorithmic Dimension

Algorithmic dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions of intersections and Cartesian products of fractals in Euclidean spaces. This approach shows that a known intersection formula for Borel sets holds for arbitrary sets...